Several experimental data support the notion that the recognition of DNA crossovers play an important role in the multiple functions of topoisomerase II. Here, a theoretical analysis of the possible modes of assembly of yeast topoisomerase II with right and left-handed tight DNA crossovers is performed, using the crystal coordinates of the docking partners. The DNA crossovers are assumed to be clamped into the central hole of the enzyme. Taking into account the rules for building symmetric ternary complexes and the structural constraints imposed by DNA-DNA and protein-DNA interactions, this analysis shows that two geometric solutions could exist, depending on the chirality of the DNA crossovers. In the first one, the two DNA segments are symmetrically recognized by the enzyme while each single double helix binds asymmetrically the protein dimer. In the second one, each double helix is symmetrically recognized by the protein around its dyad axis, while the two DNA segments have their own binding modes. The finding of potential DNA-binding domains which could interact with the crossovers provides structural supports for each model. The structural similarity of a loop containing a cluster of conserved basic residues pointing into the central hole of topoisomerase II and the second DNA-binding site of histone H5 which binds DNA crossover is of particular interest. Each solution, which is consistent with different sets of experimental data found in the literature, could either correspond to different functions of the enzyme or different steps of the reaction. This work provides structural insights for better understanding the role of chirality and symmetry in topoisomerase II-DNA crossover recognition, suggests testable experiments to further elucidate the structure of ternary complexes, and raises new questions about the relationships between the mechanism of strand-passage and strand-exchange catalyzed by the enzyme.